Whenever two opposing forces collide on the world map, a battle will commence. At the start of the battle, you'll be shown the number of forces you and your opponents have (listed in the same order as used in the preceding section), and you'll have the option of fighting the battle manually (the first option) or having the computer command all forces (the second option). Never choose the auto-battle option, because doing so will almost always result in more casualties for your side than for the opponents, and you'll never be able to win when outnumbered.
Assuming you fight the battle yourself, you'll have to decide how you want your army to align. The proper setup depends largely on what kind of forces the opponents have - in particular, the number of cannons available for each side. However, it's useful to know that the enemy always lines up in about the same way, with cannons positioned near the middle.
When your army is stronger than the enemy's
In this situation, the best strategy, attack all-out while trying to avoid sacrificing any more troops than necessary. If there's an enemy cannon, be sure to charge forward and take it out quickly, since cannon fire can quickly wipe out the central forces that you'll need to have in order to strike the heart of enemy ranks. Make optimal use of your artillery and cavalry, and try to leave a few foot soldiers around your cannons to reduce the chances of enemy troops destroying your artillery - after all, you want to be able to get as much use out of your cannons as possible. Get a few troops on the flank if the enemy general decides to evacuate there, but that won't be a concern if you can get a quick surge through the enemy defenses.
When you're much stronger than the enemy, you might find it preferable to avoid damaging enemy artillery and cavalry units, especially if those enemy units overpursue. That's because you can confiscate leftover cannons and horses at the end of the battle and use them yourself in future fights!
When your army is roughly the same strength as the enemy's
Probably the most conventional approach is to position your cannons in the center and hope that your big guns will outlast your opponent's artillery and allow you to blast your way through the enemy defenses. There's a degree of risk to this approach, however, because if the enemy cannons get the first shot (which happens a lot), you might lose your own cannons and be forced to flee to the flank and/or lose any troops positioned near the middle of the battlefield. Flank attacks can work well against a foe of similar strength, since this strategy will keep your men away from enemy cannon fire. The downside is that battles fought in this way - especially with the extreme two-flank formation will often take a much longer time to develop, increasing the risk of your opponents being able to earn enough time to launch an offensive on your own general.
Either way, don't completely abandon any part of the battlefield. The enemy general is faster than most of your troops, so you'll lose in the event of a footrace. If you can surround the enemy leader on multiple sides, however, he'll have nowhere to run and nowhere to hide.
When your army is weaker than the enemy's
Just because your forces are outmanned by the enemy doesn't mean you can't fight valiantly and put a serious dent in your enemy's most critical defenses. In fact, it's even possible to win in such situations, even as a heavy underdog, if you use good strategy and get a bit of luck on your side. Flank attacks are usually the way to go when outmanned, especially if the enemy has ample artillery forces. Be patient, and position some grenadiers a reasonable distance from the enemy troops so you can knock out a bunch of enemies from afar without much risk. Watch for any opportunity to strike at the enemy general, even if it's from an unusual angle, like the back or flank. Fight to the last man, and if you lose your last regular troop, take control of your general and launch one last swipe at the enemy's artillery or general.
If you don't have any chance of winning, organize your regiment into two flanks, then send as many troops as possible to the enemy's center and take out as many cannons as possible. This way, if you have to fight this same regiment again, you'll have a much, much easier time winning.
At the start of the battle, your first action should be to locate your general and move him away from the back center of the battlefield, where your general could be exposed if the enemy's artillery breaks through. I've won several battles against a stronger force by breaking through the ranks and blasting the enemy general with a couple of cannonballs. Generally the safest place for the general is in either back corner of the field. Keep a couple of officers and a few foot soldiers nearby to help protect your general, and if a group of enemy soldiers starts getting too close for comfort, be ready to flee to the opposite side of the battlefield.